




'''simple docstring'''



from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray







def       _UpperCamelCase			(_lowerCamelCase				:  float ,						_lowerCamelCase				:  float ,						_lowerCamelCase				:  bool = False						)-> list[float]:




     '''simple docstring'''





     if radian_mode:
          return [magnitude * cos(_lowerCamelCase						), magnitude * sin(_lowerCamelCase						)]
     return [magnitude * cos(radians(_lowerCamelCase						)						), magnitude * sin(radians(_lowerCamelCase						)						)]







def       _UpperCamelCase			(_lowerCamelCase				:  NDArray[floataa] ,						_lowerCamelCase				:  NDArray[floataa] ,						_lowerCamelCase				:  float = 10**-1						)-> bool:




     '''simple docstring'''





     __snake_case            =	cross(_lowerCamelCase ,						_lowerCamelCase						)
     __snake_case            =	sum(_lowerCamelCase						)
     return abs(_lowerCamelCase						) < eps


if __name__ == "__main__":
     # Test to check if it works
     UpperCAmelCase_							:	List[str]	     =		array(
         [
             polar_force(718.4, 1_8_0 - 3_0),
             polar_force(879.54, 4_5),
             polar_force(1_0_0, -9_0),
         ]
     )

     UpperCAmelCase_							:	NDArray[floataa]	     =		array([[0, 0], [0, 0], [0, 0]])

     assert in_static_equilibrium(forces, location)

     # Problem 1 in image_data/2D_problems.jpg
     UpperCAmelCase_							:	str	     =		array(
         [
             polar_force(3_0 * 9.81, 1_5),
             polar_force(2_1_5, 1_8_0 - 4_5),
             polar_force(2_6_4, 9_0 - 3_0),
         ]
     )

     UpperCAmelCase_							:	Optional[Any]	     =		array([[0, 0], [0, 0], [0, 0]])

     assert in_static_equilibrium(forces, location)

     # Problem in image_data/2D_problems_1.jpg
     UpperCAmelCase_							:	List[Any]	     =		array([[0, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

     UpperCAmelCase_							:	int	     =		array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

     assert in_static_equilibrium(forces, location)

     import doctest

     doctest.testmod()








"""simple docstring"""






import timeit

import numpy as np

import datasets
from datasets.arrow_writer import ArrowWriter
from datasets.features.features import _ArrayXD




def __magic_name__	(				_lowerCamelCase:		Optional[Any]			)					->						Dict:

	'''simple docstring'''




	def wrapper(*_lowerCamelCase:		Any,					**_lowerCamelCase:		Union[str, Any]			):
		lowerCAmelCase												=  timeit.default_timer()
		lowerCAmelCase												=  func(*_lowerCamelCase,					**_lowerCamelCase			)
		lowerCAmelCase												=  timeit.default_timer() - starttime
		return delta

	lowerCAmelCase												=  func.__name__

	return wrapper




def __magic_name__	(				_lowerCamelCase:		dict,					_lowerCamelCase:		List[Any]=100,					_lowerCamelCase:		int=None			)					->						List[Any]:

	'''simple docstring'''




	lowerCAmelCase												=  []
	lowerCAmelCase												=  seq_shapes or {}
	for i in range(_lowerCamelCase			):
		lowerCAmelCase												=  {}
		for col_id, (k, v) in enumerate(features.items()			):
			if isinstance(_lowerCamelCase,					_ArrayXD			):
				lowerCAmelCase												=  np.random.rand(*v.shape			).astype(v.dtype			)
			elif isinstance(_lowerCamelCase,					datasets.Value			):
				if v.dtype == "string":
					lowerCAmelCase												=  '''The small grey turtle was surprisingly fast when challenged.'''
				else:
					lowerCAmelCase												=  np.random.randint(10,					size=1			).astype(v.dtype			).item()
			elif isinstance(_lowerCamelCase,					datasets.Sequence			):
				while isinstance(_lowerCamelCase,					datasets.Sequence			):
					lowerCAmelCase												=  v.feature
				lowerCAmelCase												=  seq_shapes[k]
				lowerCAmelCase												=  np.random.rand(*_lowerCamelCase			).astype(v.dtype			)
			lowerCAmelCase												=  data

		dummy_data.append((i, example)			)

	return dummy_data




def __magic_name__	(				_lowerCamelCase:		Tuple,					_lowerCamelCase:		Tuple,					_lowerCamelCase:		Union[str, Any]=100,					_lowerCamelCase:		List[Any]=None			)					->						List[Any]:

	'''simple docstring'''




	lowerCAmelCase												=  generate_examples(_lowerCamelCase,					num_examples=_lowerCamelCase,					seq_shapes=_lowerCamelCase			)

	with ArrowWriter(features=_lowerCamelCase,					path=_lowerCamelCase			) as writer:
		for key, record in dummy_data:
			lowerCAmelCase												=  features.encode_example(_lowerCamelCase			)
			writer.write(_lowerCamelCase			)

		lowerCAmelCase							,       lowerCAmelCase												=  writer.finalize()

	if not num_final_examples == num_examples:
		raise ValueError(
		    F"""Error writing the dataset, wrote {num_final_examples} examples but should have written {num_examples}."""			)

	lowerCAmelCase												=  datasets.Dataset.from_file(filename=_lowerCamelCase,					info=datasets.DatasetInfo(features=_lowerCamelCase			)			)

	return dataset


